how do you find the radius of a circle when given the central angle and arc length
arc length = 82 central angle = 135 degrees

The area of the circle, using 3.14 to approx. The area of this circle is 615.44[tex]ft^{2}[/tex].

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = [tex]\pi r^{2}[/tex], where r is the circle's radius, is the formula for calculating a circle's surface area.

The square unit—for instance, [tex]m^{2}, cm^{2}, in^{2}[/tex] etc.—is the unit of area. In square units, the area of a circle is equal to [tex]\pi r^{2}[/tex]or [tex]\frac{\pi d^{2} }{4}[/tex]where (Pi) = [tex]\frac{22}{7}[/tex] or 3.14. The ratio of a circle's circumference to its diameter is known as pi (π). This unique mathematical constant exists.

Area = [tex]\pi r^{2}[/tex]

3.14×14×14 = 615.44[tex]ft^{2}[/tex].

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If a gardener can care for the greens property in 5 hours and if his helper assists him, they will be done in 4 hours, then the number of hours it takes for the helper to do it alone is equal to 20.

The number of hours it takes for the helper to do it alone can be found as follows;

Time taken by both the gardener and the helper to complete the job=4

Work done by both the gardener and the helper in one hour = 1/4

Similarly,

Time taken by the gardener to complete the job = 5

Work done by the gardener in one hour = 1/5

The number of hours it takes for the helper alone can be calculated by subtraction. Subtracting the fraction done by the gardener in 1 hour from the fraction done by both the gardener and the helper in 1 hour;

1/4 - 1/5

As the common denominator is 20, we multiply 1/4 by 5 and 1/5 by 4.

5/20 - 4/20 = 1/20

The number of hours it takes for the helper to do it alone can be found by finding the reciprocal of 1/20 which is equal to 20/1

20/1 = 20

Hence, the helper takes 20 hours to do it alone.

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Given - Sides of a triangle

Find - Value of x

Solution - The value of x is 3.

The sides of the right angled triangle are calculated by the Pythagoras theorem. As per the theorem,

Hypotenuse² = Base² + Perpendicular²

In the given triangle, Hypotenuse is (x+2), Perpendicular is 5 and Base is (x-3).

(x+2)² = 5² + (x-3)²

x² + 4x + 4 = 25 + x² - 6x + 9

On solving, the equation will be -

6x + 4x = 25 + 9 - 4

Performing addition and subtraction to find the value of x

10x = 30

x = 30/10

Performing division to find the value of x

x = 3

So, the value of x is 3.

The tracts of land in the study is the Control group.

The tracts of land in the study are reforested using the previous best practice whose results are already known. Now, it is not known, how the proposed method of reforestrey to plant a variety of trees at different intervals would grow. So, the tracts of land of previous plant can serve as a standard to which comparisons can made as to whether the newly proposed method is performing better than the previous or not.

This study was conducted at the Agua Salud Project site located in the Panama Canal Watershed (9° 13 N′, 79° 47′ W, 33 m amsl) with an average rainfall of 2700 mm annually, 80% of which falls between May and mid-December. Mean daily maximum and minimum temperatures are 32 °C and 23 °C . The topography is characterized by short and steep slopes. Soils are silt clay to clay with pH values of 4.4 to 5.8 and have very low levels of both plant available and total phosphorus. The data were collected from the Agua Salud native species and T. grandis plantation, both established in 2008 and planted in the same 3 m by 3 m spacing configuration.

Despite this information, changing landowners’ perceptions and transitioning from one species to a lesser known one, is a risk for the landowner and may require financial incentives.

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Answer:

x [tex]\leq[/tex]-1

Step-by-step explanation:

first distribute

24+28.8x-21.6[tex]\leq[/tex]-26.4

add like numbers

2.4+28.8x[tex]\leq[/tex]-26.4

move the constant to the right

28.8x[tex]\leq[/tex]-26.4-2.4

calculate

28.8x[tex]\leq[/tex]-28.8

divide both sides by 28.8

x[tex]\leq[/tex]-1

The height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² = 2 m

Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .

Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.

Formula of potential energy :

U = mgh

where, U = gravitational energy

            m = mass of object

            g = gravitational acceleration

            h = vertical height  of object

In the question given,

g= -9.8m/s² , U = -39.2 kg m² /s²

as, U = mgh

   h = U / mg

  put the values in this equation

  h = -39.2 / 2 (-9.8 )

 h = 2

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The complete question is :

On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .

a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?

b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?

The required number line representation is attached

To solve this question we need to know the concept of number line :

Number lines are a horizontal straight lines in which the integers are placed in equal intervals all this numbers in a sequence can be represented in a number line . this line extends infinitely in both sides.

the numbers on the number line increases as one move right and decreases on moving from right to left . A number line can be used to depict both positive and negative integers. Writing numbers on a number line facilitates number comparison. The numbers on the left of the number line are smaller than the numbers on the right.

A number line can also be used to carry out addition , subtraction , multiplication and division . We move right to add move left to subtract and skip count to multiply .

The required number line is attached in the picture below :  

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The triangle with side lengths of 57 yards, 74 yards, and 95 yards is not a right triangle because it does not obey Pythagoras theorem.

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem shows the relationship between sides of a right triangle. It states that for a right angled triangle:

Hypotenuse² = Leg1² + Leg2²

To prove that a triangle with side lengths of 57 yards, 74 yards, and 95 yards is a right triangle:

95² = 74² + 57²

9025 = 5476 + 3249

9025 ≠ 8725

The triangle with side lengths of 57 yards, 74 yards, and 95 yards is not a right triangle because it does not obey Pythagoras theorem.

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Answer: 60%

Step-by-step explanation:

12/20=.6

.6 is 60%

Answer:

21

Step-by-step explanation:

Answer:

113 explanation I just took the test

Answer: 113

Step-by-step explanation:

100 + 10 +5 -10 +8 = 113

8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.

Given: 8 +  [tex]10^x[/tex] = 1008

=>  [tex]10^x[/tex] = 1000

=>  [tex]10^x[/tex] = 10³

=> x = 3

Hence, 8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.

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In order to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.

It should be noted that this is a pie chart and the information shows the percentage for each group.

In this case, to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.

For example, berry will be:

= 15.4% × 632

= 97

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Step-by-step explanation:

I guess the question really is how much weight of dog food do you have.

1 bag = 51/2 pounds

334 bags = 334 × 1 bag = 334×51/2 = 167×51 =

= 8,517 pounds

The function fg(x) seems to be the product of f and g, whereas the function fog(x) is the composition of f and g.

A function whose values are discovered by applying another function to an independent variable and then applying that second function to the result, and whose domain consists of those possible values for which the result yielded by the first function lies inside the domain of both the second.

A composite function is one that is dependent on another. When one function is swapped for another, a composite function is formed. For example, f(g(x)) is the composite function created when g(x) is replaced for x in f. (x). f(g(x)) can be translated as "f of g of x."

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Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.

When two angles have measures adding to up to 90 degrees, they are called complementary .

Given that;

For complimentary angles;

m∠ADB + m∠BDC = 90°

Plug in the given values and solve for a.

( 3a + 10 ) + 13a = 90

3a + 10 + 13a = 90

10 + 16a = 90

16a = 90 - 10

16a = 80

a = 80/16

a = 5

Now, find the measure of ∠ADB and ∠BDC.

m∠ADB = ( 3a + 10 ) = 3(5) + 10 = 15 + 10 = 25°

m∠BDC = 13a = 13( 5 ) = 65°

Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.

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Solution of the equation for G is given as G =  Fr²/Mm

According to the question we have been given the formula for evaluating the value of F which is given as :

                           F = GmM/r²

Now we need to solve the equation for evaluating G. Which is given step by step as :

                        F = GmM/r²

Multiplying both the sides by r² we get

                       Fr² = GmM*r²/r²

                       Fr² = GmM

dividing both the sides by Mm we get

                        Fr²/Mm = GmM/Mm

                        Fr²/Mm = G

                   or, G =  Fr²/Mm

Hence the solution for G is given as   G =  Fr²/Mm

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If Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. The number of cans of paint that Tim buy is: 6 cans.

Let x represent the number of can

Quantity of addictive mixed in each liter=3/8

Total addictive mixed=3/4

Hence,

x(3/8)=3/4

Cross multiply

x=8(3/4)

x=6 cans of paint

Therefore If Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. The number of cans of paint that Tim buy is: 6 cans.

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UIF stands for Unemployment Insurance Fund.

Thus this is the full form of UIF.

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Answer:

Letter D is the correct answer.

Step-by-step explanation:

In the graph, the first line is an increasing diagonal and it stops in 10, meaning that John travelled 10 miles in 10 minutes.

After that, there is a horizontal line that indicates how much time he spent at the restaurant.

Finally, the last diagonal shows the distance travelled (5 miles) and the time it took (10 minutes.)

had the same question a couple minutes ago

hope it helps you;)

The system of inequalities are 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Total amount by washing cars = 10x

Total amount by tutoring = 22y

Total hours should be no less than 8

So,

x + y ≥ 8

And,

Total amount ≥ 10

10x + 22y ≥ 10

By substitution,

10(8 - y) + 22y ≥ 10

y ≥ 2.5

And x ≥ 5.5

Hence "The system of inequalities is 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively".

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Answer:

........................................

Answer:FIRST ONE

Step-by-step explanation:

The prime decomposition is [tex]5^{2}[/tex]×61.

Prime factor decomposition of a number means writing it as a product of prime factors. To factorize a number, divide it by the first possible prime number. Take a resulting quotient below the number.

Therefore the prime decomposition is

       [tex]5^{2}[/tex] × 61

Here 5 and 61 is a prime number .

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The measure of the angle 1, 2, and 3 will be 54°, 45°, and 81°, respectively.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The initial angle of a triangle is measured by multiplying a value by six. The second angle's measurement is nine less than the first angle's. The third angle's measure is three times greater than the first angle's measurement. Let x be the number. Then the measure of the angle 1, 2, and 3 will be

∠1 = 6x

∠2 = 6x - 9

∠3 = 3x + 6x

The sum of all angles will be 180°, then the equation will be

∠1 + ∠2 + ∠3 = 180°

6x + 6x - 9 + 3x + 6x = 180°

21x = 189°

x = 9°

Then the measure of the angles will be

∠1 = 6x = 6 × 9 = 54°

∠2 = 6x - 9 = 6 × 9 - 9 = 45°

∠3 = 3x + 6x = 9x = 9 × 9 = 81°

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Brian can play only 9 games

Brian goes to the arcade with $20

The arcade charges $2 per game and $1.50 entrance fee

The equation can be represented as follows

20-1.50= 2x

18.5 = 2x

divide by the coefficient of x which is 2

x= 18.5/2

x= 9.25

Hence Brian will be able to plat only 9 games

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Answer:

1. -12

2. 20

3.-1/2

4. -9

5. 4

Step-by-step explanation:

1. -2(5+1) = -12

2. 3(5+2)-1 = 21-1 = 20

3. -5/10 = -1/2

4. 1-4(5/2) = 1-20/2 = 1-10 = 9

5. 2(5-3) = 4

The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²

Area of ay trapezoid is determined using the formula:

Area = 1/2 × (a + b) × h, where a and b are the lengths of the bases of the trapezoid that are parallel, and h is the height or distance between the bases of the trapezoid.

What is the Area of a Triangle?

To find the area of a triangle, use:

Area = 1/2 × base × height of the triangle.

The area of the shaded region = area of the trapezoid - area of the triangle

Area of the trapezoid:

a = 5 m

b = 9 m

h = 6m

Substitute

Area of the trapezoid = 1/2 × (5 + 9) × 6

Area of the trapezoid = 1/2 × (14) × 6

Area of the trapezoid = 7 × 6

Area of the trapezoid = 42 m²

Area of the triangle:

Base = 7 m

Height = 6 - 4 1/2 = 1.5 m

Substitute

Area of triangle = 1/2 × 7 × 1.5

Area of triangle = 5.25 m².

The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²

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The given expression log₅32 is equivalent to the expression (D) log32/log5.

To find which expression is equivalent to log₅32:

Law of logarithms:

Given the log function, which is written as log₅32

Substitute as: log₅32 = log32/log5

Therefore, the given expression log₅32 is equivalent to the expression (D) log32/log5.

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Answer: $3.70

Step-by-step explanation:

30 divided by 8.10 equals 3.70